Find the solution of \(\frac{∂u}{∂x}=36 \frac{∂u}{∂t}+10u \) if \( \frac{∂u}{∂x} (t=0)=3e^{-2x} \) using the method of separation of variables.

• A. \(\frac{-3}{2} e^{-2x} e^{-t/3}\)
• B. \(3e^x e^{-t/3} \)
• C. \(\frac{3}{2} e^{2x} e^{-t/3} \)
• D. \(3e^{-x} e^{-t/3} \)